International Journal of Antimicrobial
Transcript of International Journal of Antimicrobial
International Journal of Antimicrobial Agents 55 (2020) 105941
Contents lists available at ScienceDirect
International Journal of Antimicrobial Agents
journal homepage: www.elsevier.com/locate/ijantimicag
Combination of polymyxin B and minocycline against
multidrug-resistant Klebsiella pneumoniae : interaction quantified by
pharmacokinetic/pharmacodynamic modelling from in vitro data
Chenyan Zhao
a , Pikkei Wistrand-Yuen
b , Pernilla Lagerbäck
b , Thomas Tängdén
b , Elisabet I. Nielsen
a , Lena E. Friberg
a , ∗
a Department of Pharmaceutical Biosciences, Uppsala University, SE-751 24 Uppsala, Sweden b Department of Medical Sciences, Section of Infectious Diseases, Uppsala University, SE-751 85 Uppsala, Sweden
a r t i c l e i n f o
Article history:
Received 23 September 2019
Accepted 5 March 2020
Editor: Jian Li
Keywords:
Polymyxin B
Minocycline
Combination therapy
Pharmacokinetic/pharmacodynamic model
In vitro time–kill study
Multidrug-resistant Klebsiella pneumoniae
a b s t r a c t
Lack of effective treatment for multidrug-resistant Klebsiella pneumoniae (MDR-Kp) necessitates finding
and optimising combination therapies of old antibiotics. The aims of this study were to quantify the
combined effect of polymyxin B and minocycline by building an in silico semi-mechanistic pharma-
cokinetic/pharmacodynamic (PKPD) model and to predict bacterial kinetics when exposed to the drugs
alone and in combination at clinically achievable unbound drug concentration–time profiles. A clinical
K. pneumoniae strain resistant to polymyxin B [minimum inhibitory concentration (MIC) = 16 mg/L] and
minocycline (MIC = 16 mg/L) was selected for extensive in vitro static time–kill experiments. The strain
was exposed to concentrations of 0.0625–48 × MIC, with seven samples taken per experiment for viable
counts during 0–28 h. These observations allowed the development of the PKPD model. The final PKPD
model included drug-induced adaptive resistance for both drugs. Both the minocycline-induced bacte-
rial killing and resistance onset rate constants were increased when polymyxin B was co-administered,
whereas polymyxin B parameters were unaffected. Predictions at clinically used dosages from the devel-
oped PKPD model showed no or limited antibacterial effect with monotherapy, whilst combination ther-
apy kept bacteria below the starting inoculum for > 20 h at high dosages [polymyxin B 2.5 mg/kg + 1.5
mg/kg every 12 h (q12h); minocycline 400 mg + 200 mg q12h, loading + maintenance doses]. This study
suggests that polymyxin B and minocycline in combination may be of clinical benefit in the treatment of
infections by MDR-Kp and for isolates that are non-susceptible to either drug alone.
© 2020 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license.
( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
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. Introduction
Management of antimicrobial resistance in multidrug-
esistant Klebsiella pneumoniae (MDR-Kp) is a major challenge
or clinicians [1] . Carbapenem-resistant and extended-spectrum
-lactamase (ESBL)-producing K. pneumoniae are listed as one
f the most critical priority pathogens by the World Health Or-
anization (WHO) ( https://www.who.int/medicines/publications/
HO- PPL- Short _ Summary _ 25Feb-ET _ NM _ WHO.pdf ). Infections
aused by these bacteria, e.g. urinary tract infections, nosocomial
neumonia and bloodstream infections, are associated with high
∗ Corresponding author. Present address: Department of Pharmaceutical Bio-
ciences, Uppsala University, P.O. Box 591, SE-751 24 Uppsala, Sweden. Tel.: + 46
8 471 4685; fax: + 46 18 471 4003.
E-mail address: [email protected] (L.E. Friberg).
K
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ttps://doi.org/10.1016/j.ijantimicag.2020.105941
924-8579/© 2020 The Author(s). Published by Elsevier B.V. This is an open access article
http://creativecommons.org/licenses/by-nc-nd/4.0/ )
ortality rates in critically ill patients [2] . Polymyxin B (PMB) and
olymyxin E (colistin) have been revived as last-resort treatment
ptions for these infections. However, the alarming increase in
esistance to polymyxins [3] necessitates optimising the use of
hese antibiotics. Polymyxin-based combination therapy has been
uggested to enhance and preserve antibacterial activity [4] . In a
revious screening experiment, minocycline (MIN) was identified
mong 13 tested old antibiotics as a promising companion drug to
MB, showing a synergistic effect [ ≥2 log 10 colony-forming unit
CFU)/mL reduction with the combination compared with its most
ctive constituent at 24 h] in four of five carbapenem-resistant
. pneumoniae clinical isolates [5] . Among the four strains, K.
neumoniae ARU613 was considered as the most refractory, be-
ng non-susceptible to both drugs with minimum inhibitory
oncentrations (MICs) of 16 mg/L both for PMB and MIN.
under the CC BY-NC-ND license.
2 C. Zhao, P. Wistrand-Yuen and P. Lagerbäck et al. / International Journal of Antimicrobial Agents 55 (2020) 105941
Table 1
Minocycline (MIN) and polymyxin B (PMB) nominal concentrations used in the
combination experiments.
Experiment no. MIN concentration (mg/L) PMB concentration (mg/L)
1 1.5 1
2 1.5 4
3 1.5 8
4 3 1
5 3 2
6 3 4
7 6 1
8 6 4
9 12 1
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In vitro time–kill studies have advantages over in vivo exper-
iments since they are less resource demanding. Their use is rec-
ommended by the European Medicines Agency (EMA) to provide
insight into exposure–effect relationships [6] . In vitro static time–
kill studies are relatively easy and inexpensive compared with dy-
namic experiments, but with the drawback that drug concentra-
tions are constant. However, by in silico semi-mechanistic pharma-
cokinetic/pharmacodynamic (PKPD) modelling, knowledge gained
from static time–kill studies can be extended to dynamic systems,
as shown for instance for Streptococcus pyogenes exposed to five
antibiotics of different classes [7] . With this approach, a range of
different dosing regimens and scenarios of interest can be com-
pared before conducting clinical studies.
PKPD modelling has additional advantages in exploring effective
drug combinations [8] . When studying combinations, the number
of possible permutations of dosages and PK profiles of interest
quickly becomes unfeasible to be tested experimentally. However,
the number of tests is in principle unlimited in model simulations.
In addition, PKPD models provide insight into the relative contri-
bution of the component drugs to the overall effect.
The aim of this study was to predict the clinical effect of PMB
and MIN against MDR-Kp, by first performing richly sampled in
vitro static time–kill studies of both drugs alone and in combi-
nation against K. pneumoniae ARU613, followed by building an in
silico PKPD model characterising the observations from these ex-
periments. Predictions were thereafter conducted by linking pub-
lished PK models to the developed PKPD model to perform Monte
Carlo simulations. This study also serves as an example where a
modelling approach is applied for translation of antibiotic effects
from in vitro to a clinical setting against a strain non-susceptible
to either antibiotic alone.
2. Materials and methods
The study was carried out stepwise. First, PMB and MIN mon-
odrug time–kill studies were conducted and PKPD models were
built based on their respective data set. Subsequently, the mon-
odrug PKPD models were combined with shared bacteria-related
parameters and were re-estimated to fit the combined monodrug
data. Predictions assuming an additive combined effect were then
made to facilitate the selection of concentrations to be tested ex-
perimentally [9] . When combination data were available, the PKPD
model was updated to fit the whole (two monodrugs + their com-
bination) data set. To note, drug adsorption to plastics [10] and
degradation were considered in the modelling. The final developed
PKPD model was linked to published PK models for MIN [11] and
PMB [12] in order to predict the combined drug effect in a simu-
lated patient population by letting the predicted unbound concen-
tration drive the drug effect.
2.1. Strains, growth media and antibiotics
A clinical OXA-48-producing MDR-Kp isolate (strain ARU613)
originating from a wound of a patient in Sweden was kindly pro-
vided by the Public Health Agency of Sweden. MICs were deter-
mined at least in duplicate by broth microdilution (for PMB), agar
dilution (fosfomycin) or a gradient method (other antibiotics; Etest,
bioMérieux, Marcy-l’Étoile, France) and the median values were
as follows: amikacin, 128 mg/L; aztreonam, 128 mg/L; cefepime,
256 mg/L; ceftazidime, 8 mg/L; ciprofloxacin, > 32 mg/L; chloram-
phenicol, > 256 mg/L; ertapenem, > 32 mg/L; fosfomycin, 256 mg/L;
gentamicin, 128 mg/L; meropenem, 32 mg/L; MIN, 16 mg/L; PMB,
16 mg/L; tigecycline, 2 mg/L; and trimethoprim, > 32 mg/L. Strain
ARU613 is thus categorised as resistant to all of the abovemen-
tioned antibiotics according to Clinical and Laboratory Standards
nstitute (CLSI) (PMB and MIN) and European Committee on An-
imicrobial Susceptibility Testing (EUCAST) (other antibiotics) clini-
al breakpoints [13,14] . Mueller–Hinton II broth and agar (BD Di-
gnostics, Sparks, MD, USA) were used as growth media. PMB
ulphate salt and MIN hydrochloride were purchased from Merck
GaA (Darmstadt, Germany). Meropenem resistance was probably
ainly caused by the presence of bla OXA-48 , and PMB resistance
y a mutation in the crrB gene (N311T) as determined by whole-
enome sequencing [5] .
Stock solutions (10 g/L) were freshly prepared by dissolving
MB in water and MIN in dimethyl sulfoxide (DMSO), and then
urther diluted to desired concentrations in water. All solutions
ere protected from light. Incremental dilutions in polypropy-
ene tubes (Falcon
TM ; BD Diagnostics) were performed to minimise
on-specific drug adsorption [10] . When experiments with DMSO
oncentrations > 1% [14] were omitted from the estimation (MIN
oncentrations of 192, 384 and 768 mg/L), similar parameter esti-
ates and visual predictive checks (VPCs) were obtained as when
hose experiments were included.
.2. Time–kill experiments
In monodrug experiments, the strain was exposed to nomi-
al PMB concentrations of 1–128 mg/L (i.e. 0.0625–8 × MIC) or
IN concentrations of 1.5–768 mg/L (i.e. ~0.1–48 × MIC), increas-
ng in a two-fold manner. Experiments were performed at least in
uplicate. Nominal concentrations of the nine selected antibiotic
airs for the combination experiments (performed in triplicate)
re listed in Table 1 . Bacterial cultures were prepared to achieve
starting inoculum in exponential growth phase of ~5 × 10 6
FU/mL. A growth control was included in every experiment, and
onodrugs (1 × MIC for PMB and 0.75 × MIC for MIN) were in-
luded in all combination experiments as a reference. Tubes were
ncubated at 37 °C with shaking at 190 rpm during the entire ex-
eriment. Samples were collected before adding antibiotics (0 h)
nd after 1, 2, 4, 8, 24 and 28 h of incubation in the presence of an-
ibiotics. Samples were serially (ten-fold) diluted before plating on
gar and then viable counts, i.e. the number of CFU on the plates,
ere counted following overnight incubation at 37 °C [9] . The limit
f detection (LOD) was 10 CFU/mL.
.3. Measured drug concentrations
Samples from bacteria-free tubes containing 0.25–8 mg/L PMB
two-fold increase) were drawn at 0 h and 4 h (in triplicate) for
rug concentration analysis. In a pilot experiment, the loss was
ound to be negligible after 4 h, in line with what has been re-
orted for colistin [10] . Each sample (200 μL) was transferred to
n Eppendorf tube filled with 200 μL of human serum (to pre-
ent further binding to the new tube [15] ) and was stored at –
0 °C until analysis. Sample preparation was performed in the
ame manner as described for colistin [15] and the sample was
uantified by liquid chromatography–tandem mass spectrometry
C. Zhao, P. Wistrand-Yuen and P. Lagerbäck et al. / International Journal of Antimicrobial Agents 55 (2020) 105941 3
Fig. 1. Schematic illustration of the final pharmacokinetic/pharmacodynamic model for polymyxin B (PMB) and minocycline (MIN) drug combination against Klebsiella pneu-
moniae. Bacteria transfer from drug-susceptible, growing state to non-susceptible, non-growing resting state (green). Antibiotic concentrations (orange) are related to the
drug-induced killing effect through rate constants ( k drug,MIN and k drug,PMB ), and the effect is diminishing by accumulated adaptive resistance ( AR ON_MIN and AR ON_PMB , yellow).
The adaptive resistance onset rate constant ( k on,MIN and k on,PMB ) increases with increasing drug concentrations. The combined antibacterial killing rate constant ( k drug,COMB ) is
dependent on k drug,MIN and k drug,PMB . In combination therapy, PMB elevated k drug,MIN and k on,MIN in a concentration-dependent manner (red dashed lines).
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LC-MS/MS) on a Sciex QTRAP 6500 LC-MS/MS system (Sciex) cou-
led to a Waters ACQUITY UPLC (ultra performance liquid chro-
atography) system (Waters Corp., Milford, MA, USA). All sam-
les were assayed on the same day. The linearity range was 0.1–10
g/L, with intrarun variability of 1–12% in the concentration range
f 0.2–10 mg/L. The PMB concentration was assumed to decrease
xponentially between 0 h and 4 h according to Eq. 1 :
dC
dt = −k d · C (1)
here the means of the measured concentrations ( C ) at 0 h and
h were used to determine the first-order rate constant ( k d ) for
ach nominal concentration. The MIN loss was set to be negligi-
le (half-life > 40 h) based on observations in a pilot experiment
here nominal drug concentrations of 3, 24 and 96 mg/L were
nalysed and the intrarun assay variability ranged between 8–14%
n the linear concentration range of 0.1–100 mg/L.
.4. In silico pharmacokinetic/pharmacodynamic model building
.4.1. Bacterial growth model
A self-limiting bacterial growth model was applied [16] . Bacte-
ia started (0 h) in the drug-susceptible, growing state (S) and were
ransferred to the non-susceptible, non-growing resting state (R) as
response to the total bacterial load. A reversal transfer was set to
as it was not supported by the data. A delay in transfer from S
o R [17] was tested. The schematic of the model can be found in
ig. 1 (green part) with differential equations ( Eq. 2 –4 ) illustrating
heir relationships.
dS
dt = k growth · S −
(k death + k drug · In h AR
)· S − k SR · S (2)
dR = k SR · S − k death · R (3)
dtSR =
S + R
B max · ( k growth − k death ) (4)
here k growth , k death and k SR are the rate constants of bacterial
rowth, death and transfer from S to R, respectively; B max is maxi-
um bacterial load; and k drug and Inh AR are drug-related parame-
ers and are discussed below.
.4.2. Monodrug modelling
The drug-related part of the model consisted of the drug killing
ate constant k drug and the inhibition of k drug owing to adaptive
esistance ( Inh AR ), as illustrated in Fig. 1 . Since similar structures
ere tested for both monodrug models, the equations below are
resented without specification for drugs, i.e. k drug and Inh AR repre-
ent either k drug,PMB and Inh AR,PMB or k drug,MIN and Inh AR,MIN . Tested
unctions for k drug were a sigmoid ( ɤ � = 1) and a basic ( ɤ = 1) E max
unction ( Eq. 5 ) and a power ( ɤ � = 1) and a linear ( ɤ = 1) function
Eq. 6 ).
drug =
E max · C γ
E C 50 γ + C γ
(5)
drug = Slope · C γ (6)
here E max is the maximum achievable antibiotic-induced killing
ate constant; EC 50 is the antibiotic concentration that results in
0% of E max ; C is the drug concentration; and Slope is the coeffi-
ient in a linear/power function.
Inh AR represents the fractional decrease of k drug and was re-
tricted to be between 0 and 1. It is a function of the accumulated
daptive resistance AR ON ( Eq. 7 ):
n h AR = ( 1 − f (A R ON ) ) β
(7)
4 C. Zhao, P. Wistrand-Yuen and P. Lagerbäck et al. / International Journal of Antimicrobial Agents 55 (2020) 105941
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where β was set to either 1 and f(AR ON ) restricted between 0 and
1, or to –1 and f(AR ON ) restricted to be negative. AR ON is one of
the two compartments that regulate resistance ( Eqs. 8 –10 ), as pre-
viously applied to colistin [9] :
dA R ON
dt = k on · A R OF F (8)
dA R OF F
dt = −k on · A R OF F (9)
k on = f (C) (10)
where AR OFF and AR ON are a pair of hypothetical adaptive resis-
tance compartments of which the sum of the amount is always
1. Bacteria were assumed to be susceptible initially ( AR OFF was 1
and AR ON was 0) and to gradually acquire resistance upon drug
exposure ( AR OFF decreased towards 0 and AR ON increased towards
1) with a rate governed by the antibiotic concentration-dependent
constant k on . A reversal transfer was not supported by the data.
Tested functions for f(AR ON ) and f ( C ) were (sigmoid) E max and lin-
ear/power functions as described above ( Eqs. 5 and 6 ) for k drug .
A pre-existing resistant subpopulation model, as applied to
meropenem [9] , was also tested for both drugs. Two distinct sub-
populations were assumed to exist in the starting inocula and the
ratio of the two populations at this time point was estimated. The
more resistant subpopulation had lower k drug and potentially lower
k growth due to a fitness cost.
2.4.3. Combined drug modelling
A basic additive interaction model ( Eq. 11 ) was used in the se-
lection of combination time–kill experiments of interest:
k drug,COMB = k drug,MIN · In h AR,MIN + k drug,PMB · In h AR,PMB (11)
where k drug,COMB is the combined drug effect; k drug,MIN and k drug,PMB
are the k drug of MIN and PMB ( Eqs. 5 and 6 ), respectively; and
Inh AR,MIN and Inh AR,PMB are the Inh AR of MIN and PMB ( Eq. 7 ), re-
spectively. After drug combination data had been generated, a gen-
eral pharmacodynamic interaction (GPDI) function [18] was tested
on various parameters such as k drug ( Eq. 12 ) and incorporated in
Eq. 11 to evaluate the PMB and MIN interaction as victim and per-
petrator drug:
k drug, v ict,COMB = k drug, v ict,MONO · (1 + f ( C perp )) (12)
where k drug,vict,MONO and k drug,vict,COMB represent the k drug of the vic-
tim drug before and after co-administration of the perpetrator drug
whose impact is a function of the drug concentration f(C perp ) . The
tested functions were as described above ( Eqs. 5 and 6 ). k drug in
Eq. 12 can be replaced by other drug-related parameters, e.g. k on .
When the two drugs are combined, the victim parameter is either
stimulated [if f(C perp ) > 0], inhibited [if –1 < f(C perp ) < 0] or un-
affected [if f(C perp ) = 0]. An empirical interaction model used by
Mohamed et al. [9] ( Eq. 8 in their article) was also tested.
2.4.4. Data analysis and model evaluation
In silico PKPD modelling was conducted using NONMEM
R © 7.4.2
with the Laplacian method. Model fit was mainly assessed by the
objective function value (OFV) ( P < 0.001, dOFV = 10.83, df. = 1).
The transform-both-sides approach was applied to estimate the
data using log 10 -transformed CFU/mL. The M3 method [19] was
used to handle data below the LOD. The residual error was de-
scribed by an additive error model, and the L2 data item [20] was
applied to handle correlations among replicate samples plated
from the same tube and time point. For nested models, the more
complex model was selected only if the OFV decreased signifi-
cantly. For non-nested models, the model with the lowest Akaike
information criteria (AIC) value (AIC = OFV + 2p, where p is the
umber of estimated parameters) was selected. The interpretabil-
ty of the model structure and the parameter values, together
ith the parameter precision, i.e. estimated relative standard errors
RSEs), were also considered. Perl-speaks-NONMEM (PsN) 4.7.15
https://uupharmacometrics.github.io/PsN/ ) was used to facilitate
odelling procedures. RStudio 3.5.1 ( http://www.rstudio.com ) was
sed for analysis visualisation.
Models were evaluated internally (with data used in the model
evelopment) and externally (with data not used in model devel-
pment) by simulation-based VPCs (10 0 0 sample size) [21] . For ex-
ernal evaluation, 22 time–kill curves from screening experiments,
ome of which were previously published [5] , on the same strain
ere explored. The concentrations used were PMB at 1 mg/L and
mg/L and MIN at 4 mg/L and 16 mg/L, alone and in combina-
ion. The sampling timepoints were 0, 1, 3, 6 and 24 h. Conse-
uently, neither the concentrations nor the timepoints were ex-
ctly the same as those used for model building.
.5. Clinical drug effect predictions
The PK model by Sandri et al. [12] was chosen for PMB since it
haracterises two-compartment kinetics and has been commonly
pplied. The PK parameters from the population with creatinine
learance ≥75 mL/min by Welling et al. [11] was chosen for MIN
ince it is the only model reporting two-compartment parame-
ers. The adopted PK model parameters are listed in Supplemen-
ary Table S1. A reported median PMB unbound drug fraction ( f u )
f 42% [12] was used. The MIN f u has been reported to be atyp-
cally concentration-dependent, i.e. decreasing f u with increasing
otal concentration [22,23] , like other members of the tetracycline
amily [24] . A log-linear model was fitted to the f u data reported
sing HEPES buffer (pH controlled at 7.4, inert from divalent metal
ons) [22] . The model (Eq. 13, Supplementary Fig. S1) indicated re-
uced f u from ~60% to 12% when the total concentration ( Ct ) in-
reased from 0.1 mg/L to 50 mg/L.
n ( f u, %) = 5 . 27 − 0 . 254 · ln ( C t , ug/L ) (13)
Considering that K. pneumoniae strain ARU613 has high MICs for
oth drugs, we chose to predict the combined drug effect based
n the highest recommended doses, i.e. a loading dose (LD) of
.5 mg/kg and a maintenance dose (MD) of 1.5 mg/kg every 12
(q12h) for PMB [25] and a LD of 400 mg and a MD of 200 mg
12h for MIN [26] . All doses were infused intravenously over 1 h in
he simulations. Additional simulated scenarios for comparison in-
luded standard doses of a LD of 2 mg/kg and a MD of 1.25 mg/kg
12h for PMB and a LD of 200 mg and a MD of 100 mg q12h for
IN; and a higher than typically used MIN dosage of 800 mg LD
apered by 10 0 mg per q12h dose until 40 0 mg [27] . Effects of
onodrug and prolonged (4 h) infusion were also explored. In all
cenarios, the starting inoculum was set to 6.8 log 10 CFU/mL and
0 0 0 patients per dosage were simulated. Interpatient variability
n the PK profiles were considered. Simulations were done in mrg-
olve ( https://mrgsolve.github.io/ ).
. Results
.1. Time–kill experiments
In total, 88 time–kill curves were performed resulting in 1277
ata points ( Fig. 2 a). A total of 41 data points were below the LOD,
ncluding 24 from MIN monodrug studies (5.2% of 460 observa-
ions), 16 from PMB monodrug studies (7.3% of 220 observations)
nd 1 from combination studies (0.2% of 597 observations).
Antibiotic effects clearly increased with increased drug con-
entrations ( Fig. 2 a). At concentrations of ≤0.5 × MIC, monodrug
ffects were marginal. At ~1 × MIC, bacterial density decreased
C. Zhao, P. Wistrand-Yuen and P. Lagerbäck et al. / International Journal of Antimicrobial Agents 55 (2020) 105941 5
Fig. 2. Visual predictive checks for the final pharmacokinetic/pharmacodynamic model by (a) internal evaluation and (b) external evaluation. The observed bacterial con-
centrations are shown as open circles (coloured according to the respective experiment). The median (solid lines) and 95% confidence interval of the median (grey shade
and black dashed lines) are defined from the data sets simulated from the model. Horizontal dashed lines indicate the limit of detection (LOD), with samples below the
LOD presented below. Time–kill experiments of each dose level were performed on two to four occasions with typically more than one replicate CFU count per time point,
defined from different dilutions. PMB, polymyxin B; MIN, minocycline.
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n the first few hours, followed by re-growth. Concentrations of
he component drugs in all combination studies were < 1 × MIC.
he improved killing effect compared with that of monodrug was
oticeable. Eight of the nine tested concentration combinations
howed synergism, defined as a ≥2 log 10 CFU/mL (mean value of
ll replicates) decrease at 24 h with the combination compared
ith the effect of the best monodrug component at the same
oncentration. The only exception was the lowest concentrations
ested (MIN 1.5 mg/L and PMB 1 mg/L), for which bacteriostasis
as observed for 8 h before re-growth occurred.
.2. Measured polymyxin B concentrations
The assayed start (0 h) concentrations were 0.14, 0.27, 0.75, 1.6,
.3 and 8.0 mg/L for the nominal concentrations of 0.25, 0.5, 1, 2,
and 8 mg/L, respectively. This indicated a trend of an increasing
xtent of drug loss with decreasing nominal concentrations during
reparation, i.e. from no loss at 8 mg/L up to 44% loss at 0.25 mg/L.
he calculated corresponding k d values were 0.175, 0.169, 0.120,
.083, 0.023 and 0.022 h
–1 , corresponding to half-lives of 4.0, 4.1,
.8, 8.4, 30 and 32 h during the 0–4 h experimental period.
6 C. Zhao, P. Wistrand-Yuen and P. Lagerbäck et al. / International Journal of Antimicrobial Agents 55 (2020) 105941
Table 2
Parameter estimates and precision of developed pharmacokinetic/pharmacodynamic model.
Parameter Description Estimated parameter (RSE) a
Bacteria-related parameters
k growth (h –1 ) Rate constant of bacterial growth 1.37 (13%)
k death (h –1 ) Rate constant of natural bacterial death 0.179 (FIX) b
B max (CFU/mL) Maximum bacterial concentration in system 10 ̂ 9.53 (1%)
T lag (h) Lag time for bacteria to transfer from S to R 0.304 (26%)
Single drug-specific parameters MIN PMB
Slope 1 (L/mg/h) Slope for power function of k drug 0.339 (27%) 0.0690 (31%)
ɤ 1 (–) Exponent for power function of k drug 0.546 (10%) 1.20 (6%)
Slope 2 (L/mg/h) Slope for linear function of k on 0.000179 (33%) 0.00402 (16%)
Slope 3 (–) Slope for linear function for AR –10.2 (43%) c 1 (FIX)
Interaction parameters (PMB affecting MIN)
E max (–) E max for interaction function of k drug,MIN,COMB 2.45 (28%)
EC 50 (mg/L) EC 50 for interaction function of k drug,MIN,COMB 0.285 (71%) c
Slope 4 (–) Slope for interaction function of k on,MIN,COMB 8.32 (27%)
ɤ 4 (–) Exponent for interaction function of k on,MIN,COMB 0.479 (43%) c
Residual error (SD, log 10 CFU/mL) 0.907 (14%)
Replicate residual error (SD, log 10 CFU/mL) 0.164 (13%)
S, susceptible compartment; R, resting compartment; MIN, minocycline; PMB, polymyxin B. a RSE, relative standard error determined in NONMEM by R –1 SR –1 (default) matrix. b k death was fixed to the value estimated in a previous study by Nielsen et al. [16] . c For parameters with reported RSE > 40%, their 95% confidence intervals were also computed by log-
likelihood profiling. Slope 3 : –6.36 to –18.3; EC 50 : 0.0996–0.551; ɤ 4 : 0.207–0.805.
3
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b
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3.3. In silico pharmacokinetic/pharmacodynamic model building
Fig. 1 shows the final PKPD model structure (NONMEM code
is available upon request). Parameter estimates are listed in Table
2 . Including a lag time for the bacteria transfer from S to R state
significantly improved the model fit (dOFV = 65, estimate 0.3 h).
k drug was best described as a power function. A (sigmoid) E max
function was not supported by the data for either drug despite the
fact that the experimental concentrations were > 10 times higher
than expected clinically. Adaptive resistance models fitted the data
somewhat better than pre-existing resistance subpopulation mod-
els with the same number of parameters (dOFV = 20 for PMB and
24 for MIN). Inh AR decreased with an increase in AR ON ( Eqs. 15 and
16 ). k on increased linearly with antibiotic concentrations in the fi-
nal model.
In h AR,PMB = 1 − A R ON,PMB (15)
In h AR,MIN = ( 1 − (−10 . 2) · A R ON,MIN ) −1
(16)
GPDI functions best described the combined drug effect. The
function with PMB as perpetrator and MIN as victim both for k drug
and k on ( Eqs. 17 and 18 ) described the drug interaction best. The
PMB impact on MIN k on ( Eq. 18 , dOFV = 135) was only significant
after PMB impact on MIN k drug ( Eq. 17 , dOFV = 133) was adopted
into the model. MIN effect on PMB was insignificant in the final
model.
k drug,M IN,COM B = k drug,MIN ·(
1 +
2 . 45 · C PMB
0 . 285 + C PMB
)(17)
k on,M IN,COM B = k on,MIN ·(1 + 8 . 32 · C PMB
0 . 479 )
(18)
According to Eqs. 17 and 18 , the killing rate constant of MIN
( k drug,MIN ) was predicted to increase 2.2-fold already at a relatively
low PMB concentration (0.285 mg/L). The predicted MIN-induced
resistance onset rate constant ( k on,MIN ) increased 5.6-fold for the
same PMB concentration. Both internal and external VPCs ( Fig. 2 )
showed overall an adequate model fit, i.e. the typical trend of the
observed data was similar to the medians in the data sets simu-
lated from the model.
.4. Clinical drug effect prediction
Both PMB and MIN as monodrugs showed marginal drug effects
t an unbound concentration of ~2 mg/L ( Fig. 3 a). In comparison, a
acterial reduction upon combining these concentrations was evi-
ent ( Fig. 3 b). At PMB LD 2.5 mg/kg + MD 1.5 mg/kg and MIN LD
00 mg + MD 200 mg, the median trend stayed below the start-
ng inoculum (bacteriostatic) for > 20 h. The 4-h infusions had neg-
igibly different CFU/mL profiles. The combined effects depended
ore on changes in MIN dose than on changes in PMB dose.
. Discussion
In this study, a PKPD modelling strategy was applied to quan-
ify the interaction between PMB and MIN against MDR-Kp from
n vitro experimental data and to predict the clinical potential
f the combination. The final PKPD model was the best based
n an extensive structural model exploration with the mechanis-
ic plausibility being considered. Mechanistically, the presented
radual decrease in antibiotic potency/efficacy, as characterised by
n adaptive resistance model, may reflect a potential combined
ffect of exposure-induced resistance gene mutation/expression,
election of subpopulations, and loss of free antibiotics ready to
xert an effect after binding to the dead cell debris. The identified
ne-way interaction model is in line with the common under-
tanding that PMB disrupts cell membrane integrity leading to
n increased intracellular MIN concentration and enhanced MIN
actericidal activity [28] . According to our model, PMB also accel-
rated resistance development against MIN. This may be because
igher intracellular MIN exposure induces more resistance directly,
r that the bacteria increase their tolerance to a higher degree
hen they are more severely affected. Despite the likely complex
echanisms of resistance and interaction in reality, a parsimonious
simple) model, with as few parameters as possible, that could
dequately and reasonably characterise the data, was our aim.
The clinical effects predicted here assumed a central PK com-
artment site of infection, e.g. bloodstream infection, and a high
acterial concentration at the start of treatment similar to the
tarting inocula (6.8 log 10 CFU/mL) in the time–kill experiments.
o further illustrate the potential contribution of the immune sys-
C. Zhao, P. Wistrand-Yuen and P. Lagerbäck et al. / International Journal of Antimicrobial Agents 55 (2020) 105941 7
Fig. 3. Predicted antibiotic and bacterial concentration profiles over time when Klebsiella pneumoniae strain ARU613 is exposed to polymyxin B (PMB) and minocycline (MIN)
(a) monodrug or (b) in combination over 36 h. Different colours in each panel represent the 50th (lines) and the 10th–90th percentile (shaded areas) profiles, i.e. prediction
intervals, of 10 0 0 simulated patients under different dosing scenarios. LD, loading dose; MD, maintenance dose; 1h, 1-h infusion; 4h, 4-h infusion. Numbers are the given
doses (in mg/kg for PMB and mg for MIN). All doses are given every 12 h (q12h). For example, PMB_LD2.5_MD1.5_1h indicates that PMB is administrated by a loading
dose of 2.5 mg/kg and a maintenance dose of 1.5 mg/kg q12h started from 12 h after the loading dose, all in a 1-h infusion. One exception is that MIN_LD80 0_MD40 0_1h
indicates an 800 mg loading dose tapered by 100 mg per administration until 400 mg q12h, i.e. 80 0, 70 0, 60 0, 50 0 mg at 0, 12, 24, 36 h, respectively, all in a 1-h infusion
in our simulation. Horizontal dashed lines in (b) indicate references for 2-log 10 killing (i.e. 4.8 log 10 CFU/mL) and burden for half saturated granulocyte-mediated killing (i.e.
6.4 log 10 CFU/mL).
t
i
t
c
s
h
8
f
t
a
l
em to the predicted CFU reduction, two reference lines are shown
n Fig. 3 b. The bacterial growth was reduced after treatment ini-
iation in all simulated combination scenarios. The median nadir
ounts were predicted to be below 6.4 log 10 CFU/mL, a threshold
uggested to correspond to when granulocyte-mediated killing is
alf saturated [29] . When the MIN dosage was increased to a LD of
00 mg followed by tapering to a MD, a 2 log 10 CFU/mL decrease
rom inoculum was reached, which would allow optimal contribu-
ion of granulocytes to bacterial clearance [29] .
PMB + MIN has potential to broaden the clinical antimicrobial
rmament against MDR-Kp infections, especially when facing iso-
ates with decreased susceptibility that would exclude monother-
8 C. Zhao, P. Wistrand-Yuen and P. Lagerbäck et al. / International Journal of Antimicrobial Agents 55 (2020) 105941
o
s
t
b
5
t
e
s
i
T
t
a
A
U
f
F
I
C
C
E
S
f
1
R
apy by either drug. This combination has been reported to have
been clinically used against Acinetobacter spp . [30] but to our
knowledge not against K. pneumoniae . Earlier in vitro studies
on polymyxins (two with colistin) + MIN against K. pneumoniae
[31–33] have all suggested a positive combined effect, although
the tested strains were susceptible to at least one of the drugs.
That polymyxin-induced nephrotoxicity and neurotoxicity could be
ameliorated by concomitant MIN [34,35] further supports the use
of this combination from a safety perspective. Nevertheless, the
predicted clinical antibacterial effects were moderate, but similar
to what could be expected for a therapy against a strain with
an MIC close to the clinical susceptibility breakpoint. It should be
noted that (i) K. pneumoniae strain ARU613 is not susceptible to
standard treatment and there would be a limited number of other
treatment options, (ii) the combination displayed a much better
effect than either drug alone, (iii) the combination is expected to
achieve a better effect on strains with lower MICs, and (iv) the im-
mune system is expected to assist in reducing the bacterial burden
[29] . The highest simulated MIN dose in this study was reported
to be safe and well tolerated in patients seeking neuroprotection
[27] , and it could consequently also be worth evaluating this dose
in infected patients.
The translational approach applied here included the following
steps:
1. in vitro time–kill studies and PKPD model building of each
component drug alone;
2. design of combination studies aiming at concentrations being
informative on the interaction;
3. conducting combination time–kill studies and exploring inter-
action functions in the PKPD model; and
4. predicting clinically achievable drug effect by linking the PKPD
model to reported clinical PK profiles.
The direct translation from in vitro to clinical effect should,
however, be interpreted with caution. Yet we have previously
demonstrated that antibacterial effects of meropenem and col-
istin can translate well from in vitro to in vivo using a model-
based strategy [36,37] and, based on these models, colistin and
meropenem in combination have been predicted in patients [9] .
We have also demonstrated the feasibility of models built on a
similar data set to predict dynamic in vitro conditions [7] , which
implies that resource-demanding dynamic systems could be saved
for verification, as a PKPD model based on static experiments can
provide the same information as dynamic experiments. The strat-
egy applied here illustrates a way to evaluate a combination iden-
tified in screening experiments by expanding the PD knowledge of
the combination in in vitro static time–kill curves and by quan-
tifying the interaction in a developed PKPD model that can sub-
sequently be applied to explore the clinical potential. In contrast
to the antibiotic PKPD index methodology, which is limited to
monodrugs and does not consider that the index can be species-
dependent owing to the different half-lives [36] , our strategy can
in a rational way forecast the relative effect of various combined
dosing regimens, also in the presence of concentration-dependent
drug interactions, as identified here. In addition, an independent
effect of a functioning immune system could be added to the
model in future explorations of translation to humans [38] .
We did not attempt to validate the presumed data-driven
mechanisms of resistance development with additional experimen-
tal data, which is a limitation of this study. Population analysis
profiling, repeated MIC determination, and genetic characterisation
of resistant populations may have shed more light on the reasons
for re-growth and potential resistance mechanisms. Another poten-
tial limitation of this study is that since only one inoculum (6.8
log 10 CFU/mL) was tested experimentally, it was not possible to
evaluate the inoculum effect or any potential drug-induced killing
f the resting bacteria. Nevertheless, the model with the same
tructure has been found to extrapolate reasonably well also when
he bacteria have been allowed to grow to high bacterial counts
efore the antibiotic is added [39] .
. Conclusions
A PKPD model including adaptive resistance and one-way (PMB
o MIN) interaction was developed to characterise the combined
ffect of PMB and MIN against MDR-Kp. The model predictions
upported this combination as being a potential treatment option
n face of difficult-to-treat isolates such as the strain studied here.
his approach has promise to translate in vitro identified effec-
ive antibiotic therapies to dosage regimens worthwhile for in vivo
nd/or clinical studies.
cknowledgment
The authors would like to thank Dr Richard Svensson [Uppsala
niversity Drug Optimization and Pharmaceutical Profiling Plat-
orm (UDOPP), Sweden] for measuring antibiotic concentrations.
unding: This work was supported by the Joint Programming
nitiative on Antimicrobial Resistance (JPIAMR), Swedish Research
ouncil [grant nos. 2015-06825 and 2015-06826 ].
ompeting interests: None declared.
thical approval: Not required.
upplementary material
Supplementary material associated with this article can be
ound, in the online version, at doi: 10.1016/j.ijantimicag.2020.
05941 .
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